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FHSST Authors
The Free High School Science Texts:
Textbooks for High School Students
Studying the Sciences
Physics
Grades 10 - 12
Version 0
November 9, 2008
ii
Copyright 2007 “Free High School Science Texts”Permission is granted to copy, distribute and/or modify this document under theterms of the GNU Free Documentation License, Version 1.2 or any later versionpublished by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in thesection entitled “GNU Free Documentation License”.
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FHSST Editors
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Whitfield
FHSST Contributors
Rory Adams ; Prashant Arora ; Richard Baxter ; Dr. Sarah Blyth ; Sebastian Bodenstein ;
Graeme Broster ; Richard Case ; Brett Cocks ; Tim Crombie ; Dr. Anne Dabrowski ; Laura
Daniels ; Sean Dobbs ; Fernando Durrell ; Dr. Dan Dwyer ; Frans van Eeden ; Giovanni
Franzoni ; Ingrid von Glehn ; Tamara von Glehn ; Lindsay Glesener ; Dr. Vanessa Godfrey ; Dr.
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Gutierrez ; Brooke Haag ; Kate Hadley ; Dr. Sam Halliday ; Asheena Hanuman ; Neil Hart ;
Nicholas Hatcher ; Dr. Mark Horner ; Robert Hovden ; Mfandaidza Hove ; Jennifer Hsieh ;
Clare Johnson ; Luke Jordan ; Tana Joseph ; Dr. Jennifer Klay ; Lara Kruger ; Sihle Kubheka ;
Andrew Kubik ; Dr. Marco van Leeuwen ; Dr. Anton Machacek ; Dr. Komal Maheshwari ;
Kosma von Maltitz ; Nicole Masureik ; John Mathew ; JoEllen McBride ; Nikolai Meures ;
Riana Meyer ; Jenny Miller ; Abdul Mirza ; Asogan Moodaly ; Jothi Moodley ; Nolene Naidu ;
Tyrone Negus ; Thomas O’Donnell ; Dr. Markus Oldenburg ; Dr. Jaynie Padayachee ;
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Yacoob ; Jean Youssef
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iii
Contents
I Introduction 1
1 What is Physics? 3
II Grade 10 - Physics 5
2 Units 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Unit Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 The Other Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Writing Units as Words or Symbols . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Combinations of SI Base Units . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Rounding, Scientific Notation and Significant Figures . . . . . . . . . . . . . . . 12
2.5.1 Rounding Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Error Margins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.3 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.4 Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Prefixes of Base Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 The Importance of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.8 How to Change Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.8.1 Two other useful conversions . . . . . . . . . . . . . . . . . . . . . . . . 19
2.9 A sanity test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.11 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Motion in One Dimension - Grade 10 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Reference Point, Frame of Reference and Position . . . . . . . . . . . . . . . . . 23
3.2.1 Frames of Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Displacement and Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Interpreting Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Differences between Distance and Displacement . . . . . . . . . . . . . . 29
3.4 Speed, Average Velocity and Instantaneous Velocity . . . . . . . . . . . . . . . . 31
v
CONTENTS CONTENTS
3.4.1 Differences between Speed and Velocity . . . . . . . . . . . . . . . . . . 35
3.5 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Description of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.6.1 Stationary Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6.2 Motion at Constant Velocity . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6.3 Motion at Constant Acceleration . . . . . . . . . . . . . . . . . . . . . . 46
3.7 Summary of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.8 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.9 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.9.1 Finding the Equations of Motion . . . . . . . . . . . . . . . . . . . . . . 54
3.10 Applications in the Real-World . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.12 End of Chapter Exercises: Motion in One Dimension . . . . . . . . . . . . . . . 62
4 Gravity and Mechanical Energy - Grade 10 67
4.1 Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1.1 Differences between Mass and Weight . . . . . . . . . . . . . . . . . . . 68
4.2 Acceleration due to Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Gravitational Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 Free fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.1 Checking units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.1 Conservation of Mechanical Energy . . . . . . . . . . . . . . . . . . . . . 78
4.5.2 Using the Law of Conservation of Energy . . . . . . . . . . . . . . . . . 79
4.6 Energy graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.8 End of Chapter Exercises: Gravity and Mechanical Energy . . . . . . . . . . . . 84
5 Transverse Pulses - Grade 10 87
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 What is a medium? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 What is a pulse? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3.1 Pulse Length and Amplitude . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.2 Pulse Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4 Graphs of Position and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.4.1 Motion of a Particle of the Medium . . . . . . . . . . . . . . . . . . . . 90
5.4.2 Motion of the Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5 Transmission and Reflection of a Pulse at a Boundary . . . . . . . . . . . . . . . 96
5.6 Reflection of a Pulse from Fixed and Free Ends . . . . . . . . . . . . . . . . . . 97
5.6.1 Reflection of a Pulse from a Fixed End . . . . . . . . . . . . . . . . . . . 97
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CONTENTS CONTENTS
5.6.2 Reflection of a Pulse from a Free End . . . . . . . . . . . . . . . . . . . 98
5.7 Superposition of Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.8 Exercises - Transverse Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Transverse Waves - Grade 10 105
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 What is a transverse wave? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.1 Peaks and Troughs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.2.2 Amplitude and Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2.3 Points in Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2.4 Period and Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2.5 Speed of a Transverse Wave . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Graphs of Particle Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.4 Standing Waves and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 118
6.4.1 Reflection of a Transverse Wave from a Fixed End . . . . . . . . . . . . 118
6.4.2 Reflection of a Transverse Wave from a Free End . . . . . . . . . . . . . 118
6.4.3 Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.4 Nodes and anti-nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.5 Wavelengths of Standing Waves with Fixed and Free Ends . . . . . . . . 122
6.4.6 Superposition and Interference . . . . . . . . . . . . . . . . . . . . . . . 125
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Geometrical Optics - Grade 10 129
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2 Light Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.1 Shadows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.2.2 Ray Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.2 Law of Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.3 Types of Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.4 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.4.1 Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.4.2 Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.4.3 Apparent Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.5 Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.5.1 Image Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.5.2 Plane Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.5.3 Ray Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.5.4 Spherical Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.5.5 Concave Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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CONTENTS CONTENTS
7.5.6 Convex Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.5.7 Summary of Properties of Mirrors . . . . . . . . . . . . . . . . . . . . . 154
7.5.8 Magnification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.6 Total Internal Reflection and Fibre Optics . . . . . . . . . . . . . . . . . . . . . 156
7.6.1 Total Internal Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.6.2 Fibre Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8 Magnetism - Grade 10 167
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2 Magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.3 Permanent magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.3.1 The poles of permanent magnets . . . . . . . . . . . . . . . . . . . . . . 169
8.3.2 Magnetic attraction and repulsion . . . . . . . . . . . . . . . . . . . . . 169
8.3.3 Representing magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . 170
8.4 The compass and the earth’s magnetic field . . . . . . . . . . . . . . . . . . . . 173
8.4.1 The earth’s magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.6 End of chapter exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9 Electrostatics - Grade 10 177
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.2 Two kinds of charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.3 Unit of charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.4 Conservation of charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.5 Force between Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.6 Conductors and insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9.6.1 The electroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9.7 Attraction between charged and uncharged objects . . . . . . . . . . . . . . . . 183
9.7.1 Polarisation of Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . 183
9.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
9.9 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10 Electric Circuits - Grade 10 187
10.1 Electric Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
10.1.1 Closed circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
10.1.2 Representing electric circuits . . . . . . . . . . . . . . . . . . . . . . . . 188
10.2 Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
10.2.1 Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
10.2.2 Potential Difference and Parallel Resistors . . . . . . . . . . . . . . . . . 193
10.2.3 Potential Difference and Series Resistors . . . . . . . . . . . . . . . . . . 194
10.2.4 Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
viii
CONTENTS CONTENTS
10.2.5 EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
10.3 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
10.3.1 Flow of Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
10.3.2 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
10.3.3 Series Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
10.3.4 Parallel Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
10.4 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
10.4.1 What causes resistance? . . . . . . . . . . . . . . . . . . . . . . . . . . 202
10.4.2 Resistors in electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . 202
10.5 Instruments to Measure voltage, current and resistance . . . . . . . . . . . . . . 204
10.5.1 Voltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
10.5.2 Ammeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
10.5.3 Ohmmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
10.5.4 Meters Impact on Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 205
10.6 Exercises - Electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
III Grade 11 - Physics 209
11 Vectors 211
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
11.2 Scalars and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
11.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
11.3.1 Mathematical Representation . . . . . . . . . . . . . . . . . . . . . . . . 212
11.3.2 Graphical Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.4 Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.4.1 Relative Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.4.2 Compass Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
11.4.3 Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
11.5 Drawing Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
11.6 Mathematical Properties of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 215
11.6.1 Adding Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
11.6.2 Subtracting Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
11.6.3 Scalar Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
11.7 Techniques of Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
11.7.1 Graphical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
11.7.2 Algebraic Addition and Subtraction of Vectors . . . . . . . . . . . . . . . 223
11.8 Components of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
11.8.1 Vector addition using components . . . . . . . . . . . . . . . . . . . . . 231
11.8.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
11.8.3 End of chapter exercises: Vectors . . . . . . . . . . . . . . . . . . . . . . 236
11.8.4 End of chapter exercises: Vectors - Long questions . . . . . . . . . . . . 237
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12 Force, Momentum and Impulse - Grade 11 239
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
12.2 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
12.2.1 What is a force? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
12.2.2 Examples of Forces in Physics . . . . . . . . . . . . . . . . . . . . . . . 240
12.2.3 Systems and External Forces . . . . . . . . . . . . . . . . . . . . . . . . 241
12.2.4 Force Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
12.2.5 Free Body Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
12.2.6 Finding the Resultant Force . . . . . . . . . . . . . . . . . . . . . . . . . 244
12.2.7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
12.3 Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
12.3.1 Newton’s First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
12.3.2 Newton’s Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . 249
12.3.3 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
12.3.4 Newton’s Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . 263
12.3.5 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
12.3.6 Different types of forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
12.3.7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
12.3.8 Forces in equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
12.3.9 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
12.4 Forces between Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
12.4.1 Newton’s Law of Universal Gravitation . . . . . . . . . . . . . . . . . . . 282
12.4.2 Comparative Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
12.4.3 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
12.5 Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
12.5.1 Vector Nature of Momentum . . . . . . . . . . . . . . . . . . . . . . . . 290
12.5.2 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
12.5.3 Change in Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
12.5.4 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
12.5.5 Newton’s Second Law revisited . . . . . . . . . . . . . . . . . . . . . . . 293
12.5.6 Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
12.5.7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12.5.8 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . 297
12.5.9 Physics in Action: Impulse . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.5.10Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
12.6 Torque and Levers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
12.6.1 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
12.6.2 Mechanical Advantage and Levers . . . . . . . . . . . . . . . . . . . . . 305
12.6.3 Classes of levers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
12.6.4 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
12.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
12.8 End of Chapter exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
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13 Geometrical Optics - Grade 11 327
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
13.2 Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
13.2.1 Converging Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
13.2.2 Diverging Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
13.2.3 Summary of Image Properties . . . . . . . . . . . . . . . . . . . . . . . 343
13.3 The Human Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
13.3.1 Structure of the Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
13.3.2 Defects of Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
13.4 Gravitational Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
13.5 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
13.5.1 Refracting Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
13.5.2 Reflecting Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
13.5.3 Southern African Large Telescope . . . . . . . . . . . . . . . . . . . . . 348
13.6 Microscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
13.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
14 Longitudinal Waves - Grade 11 355
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
14.2 What is a longitudinal wave? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
14.3 Characteristics of Longitudinal Waves . . . . . . . . . . . . . . . . . . . . . . . 356
14.3.1 Compression and Rarefaction . . . . . . . . . . . . . . . . . . . . . . . . 356
14.3.2 Wavelength and Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . 357
14.3.3 Period and Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
14.3.4 Speed of a Longitudinal Wave . . . . . . . . . . . . . . . . . . . . . . . 358
14.4 Graphs of Particle Position, Displacement, Velocity and Acceleration . . . . . . . 359
14.5 Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
14.6 Seismic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
14.7 Summary - Longitudinal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
14.8 Exercises - Longitudinal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
15 Sound - Grade 11 363
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
15.2 Characteristics of a Sound Wave . . . . . . . . . . . . . . . . . . . . . . . . . . 363
15.2.1 Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
15.2.2 Loudness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
15.2.3 Tone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
15.3 Speed of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
15.4 Physics of the Ear and Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
15.4.1 Intensity of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
15.5 Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
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15.6 SONAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
15.6.1 Echolocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
15.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
15.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
16 The Physics of Music - Grade 11 373
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
16.2 Standing Waves in String Instruments . . . . . . . . . . . . . . . . . . . . . . . 373
16.3 Standing Waves in Wind Instruments . . . . . . . . . . . . . . . . . . . . . . . . 377
16.4 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
16.5 Music and Sound Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
16.6 Summary - The Physics of Music . . . . . . . . . . . . . . . . . . . . . . . . . . 385
16.7 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
17 Electrostatics - Grade 11 387
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
17.2 Forces between charges - Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . 387
17.3 Electric field around charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
17.3.1 Electric field lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
17.3.2 Positive charge acting on a test charge . . . . . . . . . . . . . . . . . . . 393
17.3.3 Combined charge distributions . . . . . . . . . . . . . . . . . . . . . . . 394
17.3.4 Parallel plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
17.4 Electrical potential energy and potential . . . . . . . . . . . . . . . . . . . . . . 400
17.4.1 Electrical potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
17.4.2 Real-world application: lightning . . . . . . . . . . . . . . . . . . . . . . 402
17.5 Capacitance and the parallel plate capacitor . . . . . . . . . . . . . . . . . . . . 403
17.5.1 Capacitors and capacitance . . . . . . . . . . . . . . . . . . . . . . . . . 403
17.5.2 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
17.5.3 Physical properties of the capacitor and capacitance . . . . . . . . . . . . 404
17.5.4 Electric field in a capacitor . . . . . . . . . . . . . . . . . . . . . . . . . 405
17.6 Capacitor as a circuit device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
17.6.1 A capacitor in a circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
17.6.2 Real-world applications: capacitors . . . . . . . . . . . . . . . . . . . . . 407
17.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
17.8 Exercises - Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
18 Electromagnetism - Grade 11 413
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
18.2 Magnetic field associated with a current . . . . . . . . . . . . . . . . . . . . . . 413
18.2.1 Real-world applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
18.3 Current induced by a changing magnetic field . . . . . . . . . . . . . . . . . . . 420
18.3.1 Real-life applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
18.4 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
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18.4.1 Real-world applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
18.5 Motion of a charged particle in a magnetic field . . . . . . . . . . . . . . . . . . 425
18.5.1 Real-world applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
18.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
18.7 End of chapter exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
19 Electric Circuits - Grade 11 429
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
19.2 Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
19.2.1 Definition of Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . 429
19.2.2 Ohmic and non-ohmic conductors . . . . . . . . . . . . . . . . . . . . . 431
19.2.3 Using Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
19.3 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
19.3.1 Equivalent resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
19.3.2 Use of Ohm’s Law in series and parallel Circuits . . . . . . . . . . . . . . 438
19.3.3 Batteries and internal resistance . . . . . . . . . . . . . . . . . . . . . . 440
19.4 Series and parallel networks of resistors . . . . . . . . . . . . . . . . . . . . . . . 442
19.5 Wheatstone bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
19.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
19.7 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
20 Electronic Properties of Matter - Grade 11 451
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
20.2 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
20.2.1 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
20.2.2 Insulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
20.2.3 Semi-conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
20.3 Intrinsic Properties and Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
20.3.1 Surplus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
20.3.2 Deficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
20.4 The p-n junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
20.4.1 Differences between p- and n-type semi-conductors . . . . . . . . . . . . 457
20.4.2 The p-n Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
20.4.3 Unbiased . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
20.4.4 Forward biased . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
20.4.5 Reverse biased . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
20.4.6 Real-World Applications of Semiconductors . . . . . . . . . . . . . . . . 458
20.5 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
IV Grade 12 - Physics 461
21 Motion in Two Dimensions - Grade 12 463
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
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21.2 Vertical Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
21.2.1 Motion in a Gravitational Field . . . . . . . . . . . . . . . . . . . . . . . 463
21.2.2 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
21.2.3 Graphs of Vertical Projectile Motion . . . . . . . . . . . . . . . . . . . . 467
21.3 Conservation of Momentum in Two Dimensions . . . . . . . . . . . . . . . . . . 475
21.4 Types of Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
21.4.1 Elastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
21.4.2 Inelastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
21.5 Frames of Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
21.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
21.5.2 What is a frame of reference? . . . . . . . . . . . . . . . . . . . . . . . 491
21.5.3 Why are frames of reference important? . . . . . . . . . . . . . . . . . . 491
21.5.4 Relative Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
21.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
21.7 End of chapter exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
22 Mechanical Properties of Matter - Grade 12 503
22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
22.2 Deformation of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
22.2.1 Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
22.2.2 Deviation from Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . 506
22.3 Elasticity, plasticity, fracture, creep . . . . . . . . . . . . . . . . . . . . . . . . . 508
22.3.1 Elasticity and plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
22.3.2 Fracture, creep and fatigue . . . . . . . . . . . . . . . . . . . . . . . . . 508
22.4 Failure and strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . 509
22.4.1 The properties of matter . . . . . . . . . . . . . . . . . . . . . . . . . . 509
22.4.2 Structure and failure of materials . . . . . . . . . . . . . . . . . . . . . . 509
22.4.3 Controlling the properties of materials . . . . . . . . . . . . . . . . . . . 509
22.4.4 Steps of Roman Swordsmithing . . . . . . . . . . . . . . . . . . . . . . . 510
22.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
22.6 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
23 Work, Energy and Power - Grade 12 513
23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
23.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
23.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
23.3.1 External and Internal Forces . . . . . . . . . . . . . . . . . . . . . . . . 519
23.3.2 Capacity to do Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
23.4 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
23.5 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . 529
23.6 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
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CONTENTS CONTENTS
24 Doppler Effect - Grade 12 533
24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
24.2 The Doppler Effect with Sound and Ultrasound . . . . . . . . . . . . . . . . . . 533
24.2.1 Ultrasound and the Doppler Effect . . . . . . . . . . . . . . . . . . . . . 537
24.3 The Doppler Effect with Light . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
24.3.1 The Expanding Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 538
24.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
24.5 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
25 Colour - Grade 12 541
25.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
25.2 Colour and Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
25.2.1 Dispersion of white light . . . . . . . . . . . . . . . . . . . . . . . . . . 544
25.3 Addition and Subtraction of Light . . . . . . . . . . . . . . . . . . . . . . . . . 544
25.3.1 Additive Primary Colours . . . . . . . . . . . . . . . . . . . . . . . . . . 544
25.3.2 Subtractive Primary Colours . . . . . . . . . . . . . . . . . . . . . . . . 545
25.3.3 Complementary Colours . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
25.3.4 Perception of Colour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
25.3.5 Colours on a Television Screen . . . . . . . . . . . . . . . . . . . . . . . 547
25.4 Pigments and Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
25.4.1 Colour of opaque objects . . . . . . . . . . . . . . . . . . . . . . . . . . 548
25.4.2 Colour of transparent objects . . . . . . . . . . . . . . . . . . . . . . . . 548
25.4.3 Pigment primary colours . . . . . . . . . . . . . . . . . . . . . . . . . . 549
25.5 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
26 2D and 3D Wavefronts - Grade 12 553
26.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
26.2 Wavefronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
26.3 The Huygens Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
26.4 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
26.5 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
26.5.1 Diffraction through a Slit . . . . . . . . . . . . . . . . . . . . . . . . . . 558
26.6 Shock Waves and Sonic Booms . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
26.6.1 Subsonic Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
26.6.2 Supersonic Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
26.6.3 Mach Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
26.7 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568
27 Wave Nature of Matter - Grade 12 571
27.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
27.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
27.3 The Electron Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
27.3.1 Disadvantages of an Electron Microscope . . . . . . . . . . . . . . . . . 577
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CONTENTS CONTENTS
27.3.2 Uses of Electron Microscopes . . . . . . . . . . . . . . . . . . . . . . . . 577
27.4 End of Chapter Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
28 Electrodynamics - Grade 12 579
28.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
28.2 Electrical machines - generators and motors . . . . . . . . . . . . . . . . . . . . 579
28.2.1 Electrical generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
28.2.2 Electric motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
28.2.3 Real-life applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
28.2.4 Exercise - generators and motors . . . . . . . . . . . . . . . . . . . . . . 584
28.3 Alternating Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
28.3.1 Exercise - alternating current . . . . . . . . . . . . . . . . . . . . . . . . 586
28.4 Capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
28.4.1 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
28.4.2 Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
28.4.3 Exercise - capacitance and inductance . . . . . . . . . . . . . . . . . . . 588
28.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
28.6 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
29 Electronics - Grade 12 591
29.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
29.2 Capacitive and Inductive Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 591
29.3 Filters and Signal Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
29.3.1 Capacitors and Inductors as Filters . . . . . . . . . . . . . . . . . . . . . 596
29.3.2 LRC Circuits, Resonance and Signal Tuning . . . . . . . . . . . . . . . . 596
29.4 Active Circuit Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
29.4.1 The Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
29.4.2 The Light Emitting Diode (LED) . . . . . . . . . . . . . . . . . . . . . . 601
29.4.3 Transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
29.4.4 The Operational Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . 607
29.5 The Principles of Digital Electronics . . . . . . . . . . . . . . . . . . . . . . . . 609
29.5.1 Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
29.6 Using and Storing Binary Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 616
29.6.1 Binary numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616
29.6.2 Counting circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617
29.6.3 Storing binary numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 619
30 EM Radiation 625
30.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
30.2 Particle/wave nature of electromagnetic radiation . . . . . . . . . . . . . . . . . 625
30.3 The wave nature of electromagnetic radiation . . . . . . . . . . . . . . . . . . . 626
30.4 Electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
30.5 The particle nature of electromagnetic radiation . . . . . . . . . . . . . . . . . . 629
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CONTENTS CONTENTS
30.5.1 Exercise - particle nature of EM waves . . . . . . . . . . . . . . . . . . . 630
30.6 Penetrating ability of electromagnetic radiation . . . . . . . . . . . . . . . . . . 631
30.6.1 Ultraviolet(UV) radiation and the skin . . . . . . . . . . . . . . . . . . . 631
30.6.2 Ultraviolet radiation and the eyes . . . . . . . . . . . . . . . . . . . . . . 632
30.6.3 X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
30.6.4 Gamma-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
30.6.5 Exercise - Penetrating ability of EM radiation . . . . . . . . . . . . . . . 633
30.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
30.8 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
31 Optical Phenomena and Properties of Matter - Grade 12 635
31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
31.2 The transmission and scattering of light . . . . . . . . . . . . . . . . . . . . . . 635
31.2.1 Energy levels of an electron . . . . . . . . . . . . . . . . . . . . . . . . . 635
31.2.2 Interaction of light with metals . . . . . . . . . . . . . . . . . . . . . . . 636
31.2.3 Why is the sky blue? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
31.3 The photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
31.3.1 Applications of the photoelectric effect . . . . . . . . . . . . . . . . . . . 640
31.3.2 Real-life applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
31.4 Emission and absorption spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 643
31.4.1 Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
31.4.2 Absorption spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
31.4.3 Colours and energies of electromagnetic radiation . . . . . . . . . . . . . 646
31.4.4 Applications of emission and absorption spectra . . . . . . . . . . . . . . 648
31.5 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
31.5.1 How a laser works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
31.5.2 A simple laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654
31.5.3 Laser applications and safety . . . . . . . . . . . . . . . . . . . . . . . . 655
31.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656
31.7 End of chapter exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
V Exercises 659
32 Exercises 661
VI Essays 663
Essay 1: Energy and electricity. Why the fuss? 665
33 Essay: How a cell phone works 671
34 Essay: How a Physiotherapist uses the Concept of Levers 673
35 Essay: How a Pilot Uses Vectors 675
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Chapter 20
Electronic Properties of Matter -
Grade 11
20.1 Introduction
We can study many different features of solids. Just a few of the things we could study arehow hard or soft they are, what are their magnetic properties or how well do they conduct heat.The thing that we are interested in, in this chapter are their electronic properties. Simply howwell do they conduct electricity and how do they do it.
We are only going to discuss materials that form a 3-dimensional lattice. This means that theatoms that make up the material have a regular pattern (carbon, silicon, etc.). We won’tdiscuss materials where the atoms are jumbled together in a irregular way (plastic, glass,rubber etc.).
20.2 Conduction
We know that there are materials that do conduct electricity, called conductors, like the copperwires in the circuits you build. There are also materials that do not conduct electricity, calledinsulators, like the plastic covering on the copper wires.
Conductors come in two major categories: metals (e.g. copper) and semi-conductors (e.g.silicon). Metals conduct very well and semi-conductors don’t. One very interesting difference isthat metals conduct less as they become hotter but semi-conductors conduct more.
What is different about these substances that makes them conduct differently? That is whatwe are about to find out.
We have learnt that electrons in an atom have discrete energy levels. When an electron is giventhe right amount of energy, it can jump to a higher energy level, while if it loses the rightamount of energy it can drop to a lower energy level. The lowest energy level is known as theground state.
energy
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second energy level
third energy levelfourth energy level
energy levels of the electrons ina single atom
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20.2 CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11
When two atoms are far apart from each other they don’t influence each other. Look at thepicture below. There are two atoms depicted by the black dots. When they are far apart theirelectron clouds (the gray clouds) are distinct. The dotted line depicts the distance of theoutermost electron energy level that is occupied.
bb
In some lattice structures the atoms would be closer together. If they are close enough theirelectron clouds, and therefore electron energy levels start to overlap. Look at the picturebelow. In this picture the two atoms are closer together. The electron clouds now overlap. Theoverlapping area is coloured in solid gray to make it easier to see.
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When this happens we might find two electrons with the same energy and spin in the samespace. We know that this is not allowed from the Pauli exclusion principle. Something mustchange to allow the overlapping to happen. The change is that the energies of the energylevels change a tiny bit so that the electrons are not in exactly the same spin and energy stateat the same time.
So if we have 2 atoms then in the overlapping area we will have twice the number of electronsand energy levels but the energy levels from the different atoms will be very very close inenergy. If we had 3 atoms then there would be 3 energy levels very close in energy and so on.In a solid there may be very many energy levels that are very close in energy. These groups ofenergy levels are called bands. The spacing between these bands determines whether the solidis a conductor or an insulator.
energy
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valence band }}}energy levels
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Energy levels of the electrons inatoms making up a solid
In a gas, the atoms are spaced far apart and they do not influence each other. However, theatoms in a solid greatly influence each other. The forces that bind these atoms together in a
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CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11 20.2
solid affect how the electrons of the atoms behave, by causing the individual energy levels of anatom to break up and form energy bands. The resulting energy levels are more closely spacedthan those in the individual atoms. The energy bands still contain discrete energy levels, butthere are now many more energy levels than in the single atom.
In crystalline solids, atoms interact with their neighbors, and the energy levels of the electronsin isolated atoms turn into bands. Whether a material conducts or not is determined by itsband structure.
valence band
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valence band
conduction band
semiconductor
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insulator
band structure in conductors,semiconductors and insulators
Electrons follow the Pauli exclusion principle, meaning that two electrons cannot occupy thesame state. Thus electrons in a solid fill up the energy bands up to a certain level (this is calledthe Fermi energy). Bands which are completely full of electrons cannot conduct electricity,because there is no state of nearby energy to which the electrons can jump. Materials in whichall bands are full are insulators.
20.2.1 Metals
Metals are good conductors because they have unfilled space in the valence energy band. Inthe absence of an electric field, there are electrons traveling in all directions. When an electricfield is applied the mobile electrons flow. Electrons in this band can be accelerated by theelectric field because there are plenty of nearby unfilled states in the band.
20.2.2 Insulator
The energy diagram for the insulator shows the insulator with a very wide energy gap. Thewider this gap, the greater the amount of energy required to move the electron from thevalence band to the conduction band. Therefore, an insulator requires a large amount of energyto obtain a small amount of current. The insulator “insulates” because of the wide forbiddenband or energy gap.
Breakdown
A solid with filled bands is an insulator. If we raise the temperature the electrons gain thermalenergy. If there is enough energy added then electrons can be thermally excited from thevalence band to the conduction band. The fraction of electrons excited in this way depends on:
• the temperature and
• the band gap, the energy difference between the two bands.
Exciting these electrons into the conduction band leaves behind positively charged holes in thevalence band, which can also conduct electricity.
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20.3 CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11
20.2.3 Semi-conductors
A semi-conductor is very similar to an insulator. The main difference between semiconductorsand insulators is the size of the band gap between the conduction and valence bands. Theband gap in insulators is larger than the band gap in semiconductors.
In semi-conductors at room temperature, just as in insulators, very few electrons gain enoughthermal energy to leap the band gap, which is necessary for conduction. For this reason, puresemi-conductors and insulators, in the absence of applied fields, have roughly similar electricalproperties. The smaller band gaps of semi-conductors, however, allow for many other meansbesides temperature to control their electrical properties. The most important one being thatfor a certain amount of applied voltage, more current will flow in the semiconductor than in theinsulator.
Exercise: Conduction
1. Explain how energy levels of electrons in an atom combine with those of otheratoms in the formation of crystals.
2. Explain how the resulting energy levels are more closely spaced than those inthe individual atoms, forming energy bands.
3. Explain the existence of energy bands in metal crystals as the result ofsuperposition of energy levels.
4. Explain and contrast the conductivity of conductors, semi-conductors andinsulators using energy band theory.
5. What is the main difference in the energy arrangement between an isolatedatom and the atom in a solid?
6. What determines whether a solid is an insulator, a semiconductor, or aconductor?
20.3 Intrinsic Properties and Doping
We have seen that the size of the energy gap between the valence band and the conductionband determines whether a solid is a conductor or an insulator. However, we have seen thatthere is a material known as a semi-conductor. A semi-conductor is a solid whose band gap issmaller than that of an insulator and whose electrical properties can be modified by a processknown as doping.
Definition: Doping
Doping is the deliberate addition of impurities to a pure semiconductor material to changeits electrical properties.
Semiconductors are often the Group IV elements in the periodic table. The most commonsemiconductor elements are silicon (Si) and germanium (Ge). The most important property ofGroup IV elements is that they 4 valence electrons.
Extension: Band Gaps of Si and Ge
Si has a band gap of 1.744 × 10−19 J while Ge has a band gap of
1.152 × 10−19 J.
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CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11 20.3
Si
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Figure 20.1: Arrangement of atoms in a Si crystal.
So, if we look at the arrangement of for example Si atoms in a crystal, they would look likethat shown in Figure 20.1.
The main aim of doping is to make sure there are either too many (surplus) or too fewelectrons (deficiency). Depending on what situation you want to create you use differentelements for the doping.
20.3.1 Surplus
A surplus of electrons is created by adding an element that has more valence electrons than Sito the Si crystal. This is known as n-type doping and elements used for n-type doping usuallycome from Group V in the periodic table. Elements from Group V have 5 valence electrons,one more than the Group IV elements.
A common n-type dopant (substance used for doping) is arsenic (As). The combination of asemiconductor and an n-type dopant is known as an n-type semiconductor. A Si crystal dopedwith As is shown in Figure 20.2. When As is added to a Si crystal, the 4 of the 5 valenceelectrons in As bond with the 4 Si valence electrons. The fifth As valence electron is free tomove around.
It takes only a few As atoms to create enough free electrons to allow an electric current to flowthrough the silicon. Since n-type dopants ‘donate’ their free atoms to the semiconductor, theyare known as donor atoms.
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Figure 20.2: Si crystal doped with As. For each As atom present in the Si crystal, there is oneextra electron. This combination of Si and As is known as an n-type semiconductor, because ofits overall surplus of electrons.
20.3.2 Deficiency
A deficiency of electrons is created by adding an element that has less valence electrons than Sito the Si crystal. This is known as p-type doping and elements used for p-type doping usuallycome from Group III in the periodic table. Elements from Group III have 3 valence electrons,one less than the semiconductor elements that come from Group IV. A common p-type dopantis boron (B). The combination of a semiconductor and a p-type dopant is known as an p-typesemiconductor. A Si crystal doped with B is shown in Figure 20.3. When B is mixed into thesilicon crystal, there is a Si valence electron that is left unbonded.
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20.3 CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11
The lack of an electron is known as a hole and has the effect of a positive charge. Holes canconduct current. A hole happily accepts an electron from a neighbor, moving the hole over aspace. Since p-type dopants ‘accept’ electrons, they are known as acceptor atoms.
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Figure 20.3: Si crystal doped with B. For each B atom present in the Si crystal, there is oneless electron. This combination of Si and B is known as a p-type semiconductor, because of itsoverall deficiency of electrons.
Donor (n-type) impurities have extra valence electrons with energies very close to theconduction band which can be easily thermally excited to the conduction band. Acceptor(p-type) impurities capture electrons from the valence band, allowing the easy formation ofholes.
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The energy level of the donor atom is close to the conduction band and it is relatively easy forelectrons to enter the conduction band. The energy level of the acceptor atom is close to thevalence band and it is relatively easy for electrons to leave the valence band and enter thevacancies left by the holes.
Exercise: Intrinsic Properties and Doping
1. Explain the process of doping using detailed diagrams for p-type and n-typesemiconductors.
2. Draw a diagram showing a Ge crystal doped with As. What type ofsemiconductor is this?
3. Draw a diagram showing a Ge crystal doped with B. What type ofsemiconductor is this?
4. Explain how doping improves the conductivity of semi-conductors.
5. Would the following elements make good p-type dopants or good n-typedopants?
A B
B P
C Ga
D As
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CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11 20.4
E In
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20.4 The p-n junction
20.4.1 Differences between p- and n-type semi-conductors
We have seen that the addition of specific elements to semiconductor materials turns them intop-type semiconductors or n-type semiconductors. The differences between n- and p-typesemiconductors are summarised in Table ??.
20.4.2 The p-n Junction
When p-type and n-type semiconductors are placed in contact with each other, a p-n junctionis formed. Near the junction, electrons and holes combine to create a depletion region.
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Figure 20.4: The p-n junction forms between p- and n-type semiconductors. The free electronsfrom the n-type material combine with the holes in the p-type material near the junction. Thereis a small potential difference across the junction. The area near the junction is called thedepletion region because there are few holes and few free electrons in this region.
Electric current flows more easily across a p-n junction in one direction than in the other. If thepositive pole of a battery is connected to the p-side of the junction, and the negative pole tothe n-side, charge flows across the junction. If the battery is connected in the oppositedirection, very little charge can flow.
This might not sound very useful at first but the p-n junction forms the basis for computerchips, solar cells, and other electronic devices.
20.4.3 Unbiased
In a p-n junction, without an external applied voltage (no bias), an equilibrium condition isreached in which a potential difference is formed across the junction.
P-type is where you have more ”holes”; N-type is where you have more electrons in thematerial. Initially, when you put them together to form a junction, holes near the junctiontends to ”move” across to the N-region, while the electrons in the N-region drift across to thep-region to ”fill” some holes. This current will quickly stop as the potential barrier is built upby the migrated charges. So in steady state no current flows.
Then now when you put a potential different across the terminals you have two cases: forwardbiased and reverse biased.
20.4.4 Forward biased
Forward-bias occurs when the p-type semiconductor material is connected to the positiveterminal of a battery and the n-type semiconductor material is connected to the negativeterminal.
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20.4 CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11
P N
The electric field from the external potential different can easily overcome the small internalfield (in the so-called depletion region, created by the initial drifting of charges): usuallyanything bigger than 0.6V would be enough. The external field then attracts more e- to flowfrom n-region to p-region and more holes from p-region to n-region and you have a forwardbiased situation. the diode is ON.
20.4.5 Reverse biased
N P
in this case the external field pushes e- back to the n-region while more holes into the p-region,as a result you get no current flow. Only the small number of thermally released minoritycarriers (holes in the n-type region and e- in the p-type region) will be able to cross thejunction and form a very small current, but for all practical purposes, this can be ignored
of course if the reverse biased potential is large enough you get avalanche break down andcurrent flow in the opposite direction. In many cases, except for Zener diodes, you most likelywill destroy the diode.
20.4.6 Real-World Applications of Semiconductors
Semiconductors form the basis of modern electronics. Every electrical appliance usually hassome semiconductor-based technology inside it. The fundamental uses of semiconductors are inmicrochips (also known as integrated circuits) and microprocessors.
Integrated circuits are miniaturised circuits. The use of integrated circuits makes it possible forelectronic devices (like a cellular telephone or a hi-fi) to get smaller.
Microprocessors are a special type of integrated circuit. (NOTE TO SELF: more is needed butI’m not that knowledgable and I’m tired of Googling...)
Activity :: Research Project : Semiconductors
Assess the impact on society of the invention of transistors, with particularreference to their use in microchips (integrated circuits) and microprocessors.
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CHAPTER 20. ELECTRONIC PROPERTIES OF MATTER - GRADE 11 20.5
Exercise: The p-n junction
1. Compare p- and n-type semi-conductors.
2. Explain how a p-n junction works using a diagram.
3. Give everyday examples of the application.
20.5 End of Chapter Exercises
1. What is a conductor?
2. What is an insulator?
3. What is a semiconductor?
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Appendix A
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